Simplify the following expression and state the condition under which the simplification is valid: $p = \dfrac{k^2 - 13k + 40}{k^2 - 5k}$
Explanation: First factor the expressions in the numerator and denominator. $ \dfrac{k^2 - 13k + 40}{k^2 - 5k} = \dfrac{(k - 8)(k - 5)}{(k)(k - 5)} $ Notice that the term $(k - 5)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(k - 5)$ gives: $p = \dfrac{k - 8}{k}$ Since we divided by $(k - 5)$, $k \neq 5$. $p = \dfrac{k - 8}{k}; \space k \neq 5$